Locally conformally flat quasi-Einstein manifolds

Giovanni Catino; Carlo Mantegazza; Lorenzo Mazzieri; Michele Rimoldi

Locally conformally flat quasi-Einstein manifolds

Differential Geometry 2014-10-10 v3

Authors: Giovanni Catino , Carlo Mantegazza , Lorenzo Mazzieri , Michele Rimoldi

Abstract

In this paper we prove that any complete locally conformally flat quasi-Einstein manifold of dimension $n\geq 3$ is locally a warped product with $(n-1)$ -dimensional fibers of constant curvature. This result includes also the case of locally conformally flat gradient Ricci solitons.

Keywords

ricci solitons einstein metrics riemannian geometry

Cite

@article{arxiv.1010.1418,
  title  = {Locally conformally flat quasi-Einstein manifolds},
  author = {Giovanni Catino and Carlo Mantegazza and Lorenzo Mazzieri and Michele Rimoldi},
  journal= {arXiv preprint arXiv:1010.1418},
  year   = {2014}
}

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